In the figure

'G' is the centre of the circle. Find the $$\angle ACB$$ when $$\angle AGB = 150^\circ$$

Given,  $$\angle AGB = 150^\circ$$

'G' is the centre of the circle

The angle subtended by an arc of a circle at its centre is twice of the angle it subtends at any point on the circumference

$$=$$>  Angle subtended by arc AB at centre G is twice the angle subtended at point C

$$=$$>  $$\angle AGB$$ = 2 $$\angle ACB$$

$$=$$>   $$150^\circ$$ = 2 $$\angle ACB$$

$$=$$>  $$\angle ACB$$ = $$\frac{150^{\circ}}{2}$$

$$=$$>  $$\angle ACB$$ = $$75^{\circ}$$

Hence, the correct answer is Option C